Equations and Properties of Circles Quiz

Test your knowledge on circle equations & properties in analytic geometry with these 21 questions. Explore standard forms, center-radius, and more!

#1

What is the standard form of the equation of a circle?

x^2 + y^2 = r^2
y = mx + b
y^2 = ax^2 + bx + c
y = a(x - h)^2 + k
#2

Which of the following is the center-radius form of the equation of a circle?

(x - h)^2 + (y - k)^2 = r^2
x^2 + y^2 = r^2
y = mx + b
y = a(x - h)^2 + k
#3

Which of the following is the equation of a circle with center (0,0) and radius 3?

x^2 + y^2 = 9
x^2 + y^2 = 3
y = 3x
y = x^2
#4

Which of the following is the equation of a circle with center (2,-5) and radius 7?

(x - 2)^2 + (y + 5)^2 = 7^2
(x + 2)^2 + (y - 5)^2 = 7
(x - 2)^2 + (y - 5)^2 = 7
(x + 2)^2 + (y + 5)^2 = 7^2
#5

What is the equation of the circle with center (1,4) and radius 3?

(x - 1)^2 + (y - 4)^2 = 3^2
(x + 1)^2 + (y - 4)^2 = 3
(x - 1)^2 + (y + 4)^2 = 3
(x + 1)^2 + (y + 4)^2 = 3^2
#6

What is the standard form of the equation of a circle with center (-2,5) and radius 4?

(x + 2)^2 + (y - 5)^2 = 16
(x - 2)^2 + (y + 5)^2 = 4
(x + 2)^2 + (y - 5)^2 = 4
(x - 2)^2 + (y + 5)^2 = 16
#7

What is the equation of the circle with center (3,-1) and radius 2?

(x - 3)^2 + (y + 1)^2 = 4
(x + 3)^2 + (y - 1)^2 = 2
(x - 3)^2 + (y + 1)^2 = 2
(x + 3)^2 + (y - 1)^2 = 4
#8

What does the radius represent in the equation of a circle?

The distance from the center to any point on the circle
The slope of the circle
The x-coordinate of the center
The y-coordinate of the center
#9

What is the equation of the circle with center (2, -3) and radius 5?

(x - 2)^2 + (y + 3)^2 = 5^2
(x + 2)^2 + (y - 3)^2 = 5
(x - 2)^2 + (y - 3)^2 = 5
(x + 2)^2 + (y + 3)^2 = 5^2
#10

What is the equation of the circle passing through the points (1,2), (3,4), and (5,6)?

(x - 1)(x - 3)(x - 5) + (y - 2)(y - 4)(y - 6) = 0
(x - 1)^2 + (y - 2)^2 = (x - 3)^2 + (y - 4)^2 = (x - 5)^2 + (y - 6)^2
x^2 + y^2 + 2x + 4y - 39 = 0
x^2 + y^2 - 10x - 12y + 39 = 0
#11

Which of the following is the center-radius form of the equation of a circle with center (4,-2) and radius 6?

(x - 4)^2 + (y + 2)^2 = 6
(x + 4)^2 + (y - 2)^2 = 36
(x - 4)^2 + (y + 2)^2 = 36
(x + 4)^2 + (y - 2)^2 = 6^2
#12

In the equation of a circle, what does the value 'h' represent?

The y-coordinate of the center
The x-coordinate of the center
The radius
The slope
#13

What is the equation of the circle with center (0,0) and passing through the point (5,12)?

x^2 + y^2 = 169
x^2 + y^2 = 144
x^2 + y^2 = 25
x^2 + y^2 = 13
#14

In the equation of a circle, what does the value 'k' represent?

The x-coordinate of the center
The y-coordinate of the center
The radius
The slope
#15

What is the general equation of a circle?

x^2 + y^2 + Dx + Ey + F = 0
x^2 - y^2 = r^2
y = mx + b
y = a(x - h)^2 + k
#16

What is the equation of a circle with center (-3,4) and passing through the point (2,1)?

(x + 3)^2 + (y - 4)^2 = 50
(x - 3)^2 + (y + 4)^2 = 50
(x + 3)^2 + (y - 4)^2 = 25
(x - 3)^2 + (y + 4)^2 = 25
#17

What is the equation of a circle with center (-1,3) and radius 5?

(x + 1)^2 + (y - 3)^2 = 25
(x - 1)^2 + (y + 3)^2 = 25
(x + 1)^2 + (y - 3)^2 = 5
(x - 1)^2 + (y + 3)^2 = 5
#18

What is the standard form of the equation of a circle in three-dimensional space?

x^2 + y^2 + z^2 = r^2
x^2 + y^2 = r^2
x^2 + y^2 + z = r
x^2 + y = r^2
#19

In the equation of a circle, what does the value 'r' represent?

The distance from the center to any point on the circle
The slope of the circle
The x-coordinate of the center
The y-coordinate of the center
#20

What is the equation of a circle with center (-2, 5) and passing through the point (1, -1)?

(x + 2)^2 + (y - 5)^2 = 40
(x - 2)^2 + (y + 5)^2 = 40
(x + 2)^2 + (y - 5)^2 = 25
(x - 2)^2 + (y + 5)^2 = 25
#21

What is the equation of the circle with center (3, 7) and radius 8?

(x - 3)^2 + (y - 7)^2 = 64
(x + 3)^2 + (y + 7)^2 = 64
(x - 3)^2 + (y + 7)^2 = 64
(x + 3)^2 + (y - 7)^2 = 64

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